Matrix Determinant Mastery

Solve the system of equations using determinants: 2x + 3y = 8, 4x - y = 3.

• The solution for the system of equations is x = 2, y = 1.

• The solution for the system of equations is x = 3, y = 2.

• The solution for the system of equations is x = 1, y = 4.

• The solution for the system of equations is x = 0, y = 0.

What is the property of determinants when a matrix is multiplied by a scalar k?

• The determinant is divided by k

• The determinant is added to k

• The determinant is squared

• The determinant is multiplied by k raised to the power of the dimension of the matrix.

Find the inverse of the matrix [2 1; 3 4] by using the formula 1/det(A) * adj(A).

• [[0.4, -0.2], [-0.6, 0.4]]

• [[0.3, -0.2], [-0.4, 0.3]]

• [[0.5, -0.3], [-0.7, 0.6]]

• [[0.2, -0.1], [-0.3, 0.2]]

If the determinant of a matrix A is 5, what is the determinant of A^T (transpose of A)?

• 0

• 25

• -5

• 5

Solve the system of equations using determinants: x + y + z = 6, 2x - y + z = 3, x + 2y - z = 2.

• The solution is x = 2, y = 3, z = 1.

• The solution is x = 3, y = 1, z = 2.

• The solution is x = 4, y = 2, z = 0.

• The solution is x = 1, y = 2, z = 3.

Calculate the determinant of the matrix [1 2 3; 0 4 5; 1 0 6].

• 10

• 15

• 22

• 18

What is the property of determinants when two rows of a matrix are interchanged?

• The determinant is divided by 2

• The determinant remains the same

• The property of determinants when two rows of a matrix are interchanged is that the determinant is multiplied by -1.

• The determinant is squared

Find the inverse of the matrix [5 2; 3 1] by using the formula 1/det(A) * adj(A).

• [[1, -2], [-3, 5]]

• [[5, 3], [2, 1]]

• [[-1, 2], [3, -5]]

• [[5, -2], [3, -1]]

If the determinant of a matrix A is -7, what is the determinant of the inverse of A?

• 1/7

• -1/7

• 0

• 7